In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean (expected value). In particular, the variance is one of the moments of a distribution. In that context, it forms part of a systematic approach to distinguishing between probability distributions. While other such approaches have been developed, those based on moments are advantageous in terms of mathematical and computational simplicity.
The variance is a parameter describing in part either the actual probability distribution of an observed population of numbers, or the theoretical probability distribution of a sample (a not-fully-observed population) of numbers. In the latter case a sample of data from such a distribution can be used to construct an estimate of its variance: in the simplest cases this estimate can be the sample variance, defined below.
The variance of a random variable or distribution is the expectation, or mean, of the squared deviation of that variable from its expected value or mean. Thus the variance is a measure of the amount of variation of the values of that variable, taking account of all possible values and their probabilities or weightings (not just the extremes which give the range).
(VERSE 1)
Oh Wicked Witch,
How you play with my mind
With a flick of your hair
And a wink of your eye
I'm right at your feet
One day it's a "yes"
And the next it's a "no"
Please make up your mind
Before you turn mine into
That of a Scarecrow's.
(PRE-CHORUS)
As time goes by
You're becoming my
Everything
Everything
(CHORUS)
You're my yellow brick road,
You light my path and lead me on.
And with every step I take,
I'm going numb; all feeling is gone.
You're becoming all I see,
I'm going blind; my mind is fading.
So let's stop now for a break here
My legs have begun to ache, dear.
(VERSE 2)
Oh Wicked Witch,
How you play with my heart
You've showed that you liked me
Right from the start
But your words say differently
Ripped out my heart
With your right hand
And with your left
You pushed on my back to lie there
Like the Tin Man
(PRE-CHORUS)
As time goes by
You're becoming my
Everything
Everything
(CHORUS)
You're my yellow brick road,
You light my path and lead me on.
And with every step I take,
I'm going numb; all feeling is gone.
You're becoming all I see,
I'm going blind; my mind is fading.
So let's stop now for a break here
My legs have begun to ache, dear.
(BRIDGE)
I'm not the spineless lion
I'll tell you to your face
It doesn't make much sense to me
How your actions and words are in
Two different places
What hurts the most,
Is what I don't understand
It's that I still love you
With all that I am
With all that I am
(CHORUS)
You're my yellow brick road,
You light my path and lead me on.
And with every step I take,
I'm going numb; all feeling is gone.
You're becoming all I see,
I'm going blind; my mind is fading.
So let's stop now for a break here
My legs have begun to ache, dear.
(CHORUS)
You're my yellow brick road,
You light my path and lead me on.
And with every step I take,
I'm going numb; all feeling is gone.
You're becoming all I see,
I'm going blind; my mind is fading.
So let's stop now for a break here
(VERSE 1)
Now stop me if you've heard this one before
And I promise I'll change my tune
But if not, I'll sing you to sleep like a songbird
And swear on my feathers it's true
So draw the shades and close your eyes
And put on your sunglasses too
Cause where we're going
The sun's still glowing
And your eyes can't adjust to all of this new
(PRE-CHORUS)
So hush, be quiet, let me speak
No, this can't wait until next week so
(CHORUS)
Hey, are you ready for this?
It's 5th finger promise, sealed with a kiss
I'm an open book,
I'm a silhouette
I'm a shade of what I used to be
So tell me once, tell me twice, and tell me again
"You and I, we were made for this"
Turn to chapter you,
And you will find chapter me
(VERSE 2)
I'm hoping these words ring true
Cause I would save my words for you
And then listen to your breathing
As we both stared at the ceiling, thinking
"Wouldn't it be great
If all the ghosts that haunted us
Stopped til daybreak?"
Cause I'm tired, oh so tired...
(PRE-CHORUS)
So hush, be quiet, let me speak
No, this can't wait until next week so
So hush, be quiet, let me speak
No, this can't wait until
(CHORUS)
Hey, are you ready for this?
It's 5th finger promise, sealed with a kiss
I'm an open book,
I'm a silhouette
I'm a shade of what I used to be
So tell me once, tell me twice, and tell me again
"You and I, we were made for this"
Turn to chapter you,
And you will find chapter me
(BRIDGE)
So on this fateful prom night
We won't have to dance in my garage
I spent 15 minutes with you
And spent the whole night thanking God
So lets ditch this after-party
And make one of our own
Just give me half an hour
And we can both be gone.
(CHORUS)
Hey, are you ready for this?
It's 5th finger promise, sealed with a kiss
I'm an open book,
I'm a silhouette
I'm a shade of what I used to be
So tell me once, tell me twice, and tell me again
"You and I, we were made for this"
Turn to chapter you,
(Verse 1)
I've been building towers
And sandcastles on the beach.
And you're telling me now
That they're not the same
But they sure act the same to me.
'Cause in a matter of time
They'll both have the same fatal flaw
Whether rock or some sand;
Whether hours or years
They're both bound someday to fall.
But the same could be said
About you and me
Because we both know
We have to leave this town eventually.
And as the time draws near
I can't help but write your name in the sand
'Cause if home is where the heart is,
Then home is where I am.
(Pre-Chorus)
So if all that was true
I'm sure that you'll ask
"Just what the hell's
Keeping you here?"
Then I'll turn to you slow
Plant a kiss on your lips
And whisper:
"That'd be you dear."
(Chorus)
You're the only reason that I
Haven't left this place
I could jump these castle walls ever since
My 16 year old days.
You're the anchor that keeps me here,
But never holds me down.
And if you wouldn't mind packing
A little bit quicker,
I'd like to get out of this city
Before it drowns
(Verse 2)
And with every minute
We get a bit further away
Far from worry or rules and so far from our fears
That we both don't know what to say
'Cause I was speechless when I saw you
And I'm speechless here today
And I guess when we're tired of this place
You'll turn to me and say
(Pre-Chorus)
"So hun I've been thinking
A lot about this;
Just what the hell's
Keeping you here?"
Then I'll turn to you slow
Give you a smile
And whisper:
"Pack your bags, dear."
(Chorus)
You're the only reason that I
Haven't left this place
I could jump these castle walls ever since
My 16 year old days.
You're the anchor that keeps me here,
But never holds me down.
And if you wouldn't mind packing
A little bit quicker,
I'd like to get out of this city
Before it drowns
(Bridge Part I)
'Cause you're the anchor that keeps me here,
But never holds me down.
You're the anchor that keeps me here,
But never holds me down.
(Bridge Part II)
So maybe if you're in the mood for it darling,
We can stay here for a while.
And maybe go down to the beach after sunset
And build sandcastles for miles.
-Repeat-
(Chorus)
You're the only reason that I
Haven't left this place
I could jump these castle walls ever since
My 16 year old days.
You're the anchor that keeps me here,
But never holds me down.
And if you wouldn't mind packing
A little bit quicker,
I'd like to get out of this city
Before it drowns
(Verse 1)
The first breath I ever took
Well frankly it took my breath away
And if I was new, then you were too
And we could take this city and raise it one day.
But oh, travesty!
Who is this man that was born in that river?
"Am I you, or am I me?"
I asked myself; as I couldn't remember.
(Chorus)
The only thing I really know
Is I've got this debt to pay
And I've been living in shame for 20 long years
Til a man came along and gave me a way
Out of this madness
That I call my life
(Or the life that I've had since that one fateful night)
And until I met you, my mind, it was set
But what price do I pay to wipe away debt?
(Verse 2)
Oh Mary, Mary, quite contrary
Won't you sing that song again?
The one with the notes that I'll remember
Up until the day that I'm dead?
Oh no, baby, please don't cry
You don't have to sing tonight
Just sit down and I'll tell you a story
Of cities in water and practical glory.
(Chorus)
The only thing I really know
Is I've got this debt to pay
And I've been living in shame for 20 long years
Til a man came along and gave me a way
Out of this madness
That I call my life
(Or the life that I've had since that one fateful night)
And until I met you, my mind, it was set
But what price do I pay to wipe away debt?
(Bridge)
So would you kindly take my hand
And pull me deeper below?
Be the weights around my ankles
When I need air, I'll let you
-Repeat-
(Chorus)
The only thing I really know
Is I've got this debt to pay
And I've been living in shame for 20 long years
Til a man came along and gave me a way
Out of this madness
That I call my life
(Or the life that I've had since that one fateful night)
And until I met you, my mind, it was set
But what price do I pay to wipe away debt?
To wipe away debt
To wipe away debt
To wipe away debt
(VERSE 1)
You find your fun in others flaws
And we find ours in this song
Although you gave yourself to darkness
We stood by you all along
Please don't lose sight of your light
We know you have it in you
I've seen creatures in the night
And I've seen rumors come true
(PRE-CHORUS)
Don't you see what you're missing?
(CHORUS)
All you see is misfit toys,
All we see is a troubled friend.
I know that this is new but
We were born off the deep end.
You seek attention from the world
Drowning your thoughts in alcohol
Downtown is your playground
You're a daily sale, it's trivial.
(VERSE 2)
You laugh and point your fingers
Yes, we are the weird ones here,
But I'd rather live and die in color
Than in a black and white smear.
We're not on a pedestal,
Or choices that we've made.
Free will's a charming curse
With effects seen everyday.
(PRE-CHORUS)
Can't you see what you're missing?
(CHORUS)
All you see is misfit toys,
All we see is a troubled friend.
I know that is new, but
We were born off the deep end.
You seek attention from the world
Drowning your thoughts in alcohol
Downtown is your playground
You're a daily sale, it's trivial.
(BRIDGE)
You were born to breathe color,
But venom drips from your lips.
You alleged heir, stop in your tracks.
I refuse your poisonous kiss.
I'll tell you time and time again,
Let's find you a better world
I see far much more for you here
Then empty bottles, little girl.
Cause with all these burning bridges
The ground you stand on's growing thin
And now you're sinking
So leave before this building caves in
And this city crumbles
Like your memories of last night
But if you really want fight…
Then we'll fight!
(CHORUS)
You saw a band of misfit toys
And now you see your best friends.
I know that this is new to you but
We were born off the deep end
You sought attention from the world,
But now you've changed it all.
So now we cross this bridge with confidence
And you shine, beautiful.